1.4.3 Boolean Algebra Flashcards
De Morgans Laws
De Morgans Laws : Break negation and change operator between literals
NOT (a AND b) –> NOT b OR NOT a
NOT (a OR b) –> NOT b AND NOT a
Distribution
Distribution :
a AND (b OR c) –> (a AND b) OR (a AND c)
a OR (b AND c) –> (a OR b) AND (a OR c)
(a U b) ^ (c U d) = (a ^ c) U (a ^ d) U (b ^ c) U (b ^ d)
Absorption
Absorption : DONT Do this - Expand and then remove
a U (a ^ b) = a
a ^ (a U b) = a
Association
Association : involve removal or addition of brackets
c AND (a AND b) = a AND (b AND c) = a AND b AND c
Commutation
Commutation : order of literals doesn’t matter
a AND b = b AND a
a OR b = b OR a
Double Negation
Double negation : 2 negation arguments cancel out
NOT NOT c = c
D-Type Flip Flops
D-Type Flip Flops : Stores the value of one bit when a signal is given.
- Logic circuit that changes value stored (Q) to data value (D) on rising edge of clock to input, value cannot be changed otherwise and is stored.
D-Type Flip Flops combined to form registers - static RAM which is a faster and more expensive memory unit - used in cache.
Adders
Half Adder : Add two bits together producing sum and carry out
Full adder : Add two bits and carry in producing sum and carry out
Ripple adders : Chains multiple full adders together to add numbers with multiple bits together.